Pinnacles for Complex Reflection Groups

2025/10/04 by Burnham-Schmidt, Aaron, González, Nicolle
#05A05 #05A15 #05E16 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.03580

Abstract

We study, characterize, and enumerate the admissible pinnacle sets of nonexceptional complex reflection groups G(m,p,n), which include all generalized symmetric groups ℤ_m \wr S_n as special cases. This generalizes the work of Davis--Nelson--Petersen--Tenner for symmetric groups S_n and González--Harris--Rojas Kirby--Smit Vega Garcia--Tenner for signed symmetric groups ℤ₂ \wr S_n. As a consequence, we prove a conjecture of González--Harris--Rojas Kirby--Smit Vega Garcia--Tenner for pinnacles of signed permutations.

Citations

• Mesas of Stirling permutations
• Pinnacle sets of signed permutations
• Pinnacle sets revisited
• Pinnacle Set Properties
• Admissible pinnacle orderings
• A formula for enumerating permutations with a fixed pinnacle set
• Descent polynomials
• The pinnacle set of a permutation
• Permutations with given peak set

Related

• Major Indices and Perfect Bases for Complex Reflection Groups
• Springer correspndence for complex reflection groups
• Projective reflection groups
• The BMM Symmetrising Trace Conjecture for Families of Complex Reflection Groups of Rank Two
• Integer Representations of the Generalized Symmetric Groups